SOLUTION: There are 3 question. 1.How do you know if a quadratic equation will have one, two,or no solutions? 2. How do you find a quadratic equation if you are only given the solution?

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Question 134718: There are 3 question.
1.How do you know if a quadratic equation will have one, two,or no solutions?
2. How do you find a quadratic equation if you are only given the solution?
3. Is it possible to have different quadratic equations with the same solution?
This information is for my college algebra class.
Thanks Roosevelt
Found 2 solutions by stanbon, vleith:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
There are 3 question.
1.How do you know if a quadratic equation will have one, two,or no solutions?
b^2-4ac is the discriminant:
if it is negative you have two complex number solutions
If it is zero you have two equal Real number solutions
If it is positive you have two Real number solutions
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2. How do you find a quadratic equation if you are only given the solution?
If solutions are "a" and "b", the equation is y = k(x-a)(x-b)
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3. Is it possible to have different quadratic equations with the same solution?
Yes because the "k" in answer #2 can have different values.
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Cheers,
Stan H.

Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website!
1) Look at the determinant part of the quadratic equation

The determinant is

If that results in a negative == no solutions (complex numbers)
If it is positive, then two roots
If it is 0, the one root two times
2) Lets say the solutions are x=5 and x= 7
Then will give a quadratic equation with those solutions
More generally, if the roots are a and b
then just multiply it out
3)Sure. One quick way to see that is to just multiply by a constant C
same root, different equation
make sense?